Compact undulator system and methods

ABSTRACT

An undulator with a compact construction is provided that reduces weight, complexity and cost. The compact undulator system and methods provides mechanical integrity without compromising magnetic field quality.

PRIORITY

This application is a continuation application of U.S. patentapplication Ser. No. 15/005,434 filed Jan. 25, 2016, which is acontinuation application of U.S. patent application Ser. No. 14/237,656filed Feb. 7, 2014, now U.S. Pat. No. 9,275,781, which claims thebenefit of International Application PCT/US12/50135 filed Aug. 9, 2012,which claims the benefit of U.S. Provisional Patent Application Ser. No.61/521,606 filed Aug. 9, 2011.

GOVERNMENT RIGHTS

The present invention was made in part with government support underDMR-0936384 and DMR-0807731 awarded by National Science Foundation. TheU.S. government has certain rights in the invention.

FIELD OF THE INVENTION

The present invention is related generally to insertion devices, andmore specifically to an undulator system and methods employing a compactconstruction that provides mechanical integrity without compromisingmagnetic field quality thereby reducing weight, complexity, and cost.

BACKGROUND

Undulators are magnetic assembly insertion devices that are used atsynchrotron radiation sources such as Free Electron Lasers (FEL) andStorage Rings. Undulators are used in the medical and industrial marketsfor x-ray or longer wavelength photon beam purposes.

Specifically, undulators include opposing magnet arrays producing aperiodic spatial magnetic field distribution in a gap between them. Ahigh-energy electron beam passing through this gap parallel to thearrays “wiggles” back and forth in its trajectory due to the periodicmagnetic field. Undulators further may include temperature-stabilizingcomponents selectively arranged to prevent a temperature-dependentchange in the magnetic field of the undulator.

Undulators are periodic magnetic structures, and their magnetic field isessentially sinusoidal. Undulators with a magnetic field in one planeare called linearly polarized undulators. Undulators known aselliptically polarized undulators have an adjustable field direction.Some other undulators have a magnetic field direction that rotates.These are known as helical undulators,

The typical undulator consists of a massive C-shaped frame, two or fourmagnet arrays, and one or more driving mechanisms. Magnet arraysattached to the frame and driving mechanisms provide precise arraysmotion, i.e. variation of the gap between them. Because forces betweenmagnet arrays are quite significant (few tons) and varying, and thetolerances on magnet array position are quite small (few microns), theC-frame must be very stiff. These requirements require large and heavystructures for the magnet arrays holding. Furthermore, undulators aretypically very expensive.

What is needed is a compact sized undulator that reduces weight,complexity, and cost and that provides mechanical integrity withoutcompromising magnetic field control and quality. The present inventionsatisfies this need.

SUMMARY

The undulator of the present invention is much smaller and lessexpensive than conventional undulators while providing similar x-raybeam intensities and variable spectra. Providing a compact undulatoraccording to the present invention is beneficial since the space aroundbeam lines where undulators are installed is very limited. Furthermore,the undulator of the present invention weighs considerably less thanconventional undulators.

According to the present invention, an undulator system and methodsincludes a rectangular box-shape frame. Miniature linear bearings orsliders are positioned within the rectangular box-shape frame and PurePermanent Magnet (PPM) arrays (otherwise simply referred to as “magnetarrays”) are fastened to the bearings. Specifically, each magnet arrayincludes a base plate and permanent magnet blocks each positioned withina holder. The base plate is fastened to the bearings and the holders aresecured to the base plate. In one embodiment, the holders are of acopper material. Each magnet block is soldered to a holder such that agap is formed between opposing magnet arrays. The photon beam using anelectron beam is generated in the gap. In addition, cooling elements areattached to the rectangular box-shape frame and to the magnet arrays inorder to control temperature of the frame and arrays. At least one ofthe magnet arrays is moveable through the use of a driving mechanismthat provides the motion of the magnet array along a beam axis. Themagnetic field strength of the undulator—specifically within theconstant gap between opposing magnet arrays—is controlled through themovement of the magnet array.

One advantage of the present invention over conventional undulators isthat the undulator is much smaller and less expensive while providingthe same functionality. Invented undulators can be easily transported,removed, and installed as well as can more easily be placed intoexisting geometries, which may facilitate facility upgrades.

An advantage of the present invention over the recently developed Deltaundulator is that the present invention provides a large horizontalopening for the electron beam, which allows the use of the undulator instorage rings as well as at Free Electron Lasers (FEL) and EnergyRecovery Linacs (ERL).

Another advantage of the present invention is the use of two magnetarrays versus four magnet arrays such as that used in the Deltaundulator.

Another advantage of the present invention is that the compact undulatorconcept may be implemented in all types of undulators including, forexample, linearly polarized undulators, elliptically polarizedundulators, and helical undulators.

These and other aspects, features, and advantages of the presentinvention will become more readily apparent from the attached drawingsand the detailed description of the preferred embodiments, which follow.

BRIEF DESCRIPTION OF THE DRAWINGS

The preferred embodiments of the invention will be described inconjunction with the appended drawings provided to illustrate and not tothe limit the invention, where like designations denote like elements,and in which:

FIG. 1 is a perspective view of an undulator according to an embodimentof the present invention;

FIG. 2 is a cross-sectional view of an undulator according to anembodiment of the present invention;

FIG. 3 is a perspective cross-sectional view of a driving mechanismaccording to an embodiment of the present invention;

FIG. 4 illustrates a graph of measured field profiles as a function ofthe upper array position according to an embodiment of the presentinvention;

FIG. 5 illustrates a graph of measured K parameters as a function of theupper array position according to an embodiment of the presentinvention;

FIG. 6 illustrates a graph of vertical magnetic field versus positionalong the magnet array according to an embodiment of the presentinvention;

FIG. 7 illustrates a graph of x-ray flux density spectra calculated forthe magnetic field measured with no displacement between magnet arraysin comparison with ideal field spectra according to an embodiment of thepresent invention;

FIG. 8 illustrates a graph of x-ray flux density spectra calculated forthe magnetic field measured with ˜6 mm (˜90° phase) displacement betweenmagnet arrays in comparison with ideal field spectra according to anembodiment of the present invention;

FIG. 9 illustrates a graph of residual gas analyzer spectra recorded atthe end of second magnet array baking cycle;

FIG. 10 illustrates a graph of measured x-ray spectra and predictedx-ray spectra for ideal undulator magnetic field according to anembodiment of the present invention;

FIG. 11 illustrates a graph of photon normalized counting rate ofphotons with 30.49 keV energy as a function of undulator phase accordingto an embodiment of the present invention; and

FIG. 12 illustrates a graph measured electron beam tune variationsversus undulator parameter K according to an embodiment of the presentinvention.

DETAILED DESCRIPTION

FIG. 1 and FIG. 2 illustrate an undulator 100 according to an embodimentof the present invention. As shown in FIG. 1, the undulator 100comprises a rectangular box-shape frame 102 and a driving mechanism 200.In an embodiment of the present invention, the frame 102 may be made ofan aluminum material, specifically, four one meter long aluminum(6061-T6 alloy) sheets with 24 mm and 30 mm thickness. The total weightof the frame may be around 35 kg. A unique feature of the rectangularbox-shape frame 102 is that the force loops are contained within asmall, stiff structure. In other words, the rectangular box-shape frame102 is much stiffer than conventionally used C-shaped frame structures.Where the large vertical forces typically result in a roll of the magnetgirders in a conventional scheme, the rectangular box-shape frame 102and lateral symmetry effectively eliminate that deformation.

Within the rectangular box-shape frame 102 is a pair of a base plates112 as shown in the cross-sectional view of an undulator 100 accordingto FIG. 2. The base plates 112 position a plurality of holders 110, eachholder with a permanent magnet block 108. Specifically, a holder 110 issecured to the base plate 112 such as by ⅛″ Outer Diameter (OD) dowelpins and is fastened to the base plate 112 with fasteners, such as two#4-40 stainless steel screws. In an embodiment of the present invention,the holder 110 is made of a copper material.

The base plate 112, holders 110, and permanent magnet blocks 108collectively form a magnet array 114. Each permanent magnet block 108 issoldered to a holder 110 so that a gap is formed between opposingpermanent magnet arrays 114, for example a 5 mm constant vertical gap.The permanent magnet blocks 108 are soldered to the holders 110 such asby a soldering technique as disclosed in U.S. Pat. No. 7,896,224 toTemnykh issued Mar. 1, 2011, incorporated herein by reference.

In an embodiment of the present invention, the permanent magnet block108 is preferably a neodymium magnet (also known as NdFeB, NIB, or Neomagnet), specifically 40UH grade with Br=1.25 Tesla and Hcj=25.0 kOe.

Miniature linear bearings 104, otherwise referred to as sliders, arepositioned within the rectangular box-shape frame 102. Each magnet array114 is fastened to the miniature linear bearings 104. Specifically, thebase plate 112 is fastened to the miniature linear bearings 104. Theminiature linear bearings 104 provide magnet array 114 motion along abeam axis (see 116 of FIG. 3 and of FIG. 1) that is perpendicular andcoplanar with axis 115 as shown in FIG. 2. This arrangement of themagnet arrays 114 on the linear sliders or bearings 104 inside of therectangular box-shape frame 102 is an advantage over conventionaldesigns of undulator insertion devices. It should be noted that theaccess to the central magnetic field region about beam axis 116 (seeFIG. 3 and FIG. 1) after the magnet arrays 114 are assembled is limited.Thus, magnet arrays 114 may be tuned individually before assembly.

Such an arrangement of the frame 102 and magnet arrays 114 and the useof the soldering technique for fastening the permanent magnet blocks 108to the holders 110 results in significant reduction of transversedimensions as well as a reduction of the weight of the undulator 100.

In an embodiment of the present invention, the linear bearings 104chosen are a single row, profiled rail, four point contact,recirculating-ball style bearing composed primarily of 440C stainlesssteel. The bearings 104 have a static load capacity of 3.5 kN and astiffness of 33 N/μm. The Polytetrafluoroethylene (PTFE) end caps of thebearings 104 may be replaced with custom fabricated bronze parts due tothe deleterious effects of radiation on the PTFE components. All rollingelements are lubricated with ultra-high vacuum (UHV) compatiblelubricant such as Krytox 16256.

There are two loading conditions considered to size the linear bearings104. The first is the maximum vertical force of 6.3 kN that occurs witha zero phase between magnet arrays 114. By geometry, this can be assumedto be equally shared among the bearings. The more limiting case is dueto the combined moment loading of the linear actuator and the equivalentvertical force. With a moment arm of 128 mm, the 6.3 kN driving forceresults in a reaction moment of 806 Nm that, when shared among the fournearest bearings with a spacing of 184 mm, requires a load capacity 2.2kN per bearing.

With the opposing magnet arrays 114, the lower magnet array 114 is fixedto the frame 102 while the upper array 114 can be moved along beam axis(see 116 of FIG. 3 and of FIG. 1) that is perpendicular and coplanarwith axis 115 by a half period (12.2 mm) by a driving mechanism 200described more fully below. The magnet array 114 motion along a beamaxis 116 (see FIG. 3 and FIG. 1) is used to control magnetic fieldstrength. To minimize high-order mode power loss, a smooth path may beprovided for the beam image current passing through the magnet array114. For example, magnet arrays 114 may be covered with nickel platedcopper foil discussed more fully below.

Cooling elements 106 attached to the magnet arrays 114 and the frame 102may be used to control the magnet array 114 and frame 102 temperatures.Two monolithic, flexible water cooling elements 106 fabricated from bent0.25″ 316SS tubing are connected to each magnet array 114 and to therectangular box-shape frame 102. In an embodiment of the presentinvention, water may be used as a coolant such that the estimatedcooling capacity is approximately 800 W/° K. In another embodiment, coldnitrogen gas may be used as a coolant such that the temperature of themagnet arrays 114 may be decreased to approximately 0° C. or lower.Cooling elements 106 decrease potential demagnetization of permanentmagnet blocks 108 by radiation caused by a high energy electronsscattered from an electron beam,

FIG. 3 illustrates a driving mechanism 200 according to an embodiment ofthe present invention. The driving mechanism 200 includes a rodcomponent 202 that is connected to the magnet array 114 through a platecomponent 204. A tube component 206, into which the rod component 202 ispositioned, is attached to the frame 102 through connecting components208. The upper magnet array 114 can be moved along beam axis 116 bypulling the rod component 202. The tube component 206 provides the pathfor the reaction forces.

It should be noted that the driving mechanism 200 shown in FIG. 3 doesnot include a vacuum vessel. It is contemplated that edge-weldedstainless steel bellows may be used to link the driving mechanism to astepper motor residing outside of the vacuum vessel in which both therod component 202 and the tube component 206 pass through the bellows tokeep the net force on the frame 102 and subsequently the magnet arrays114 near zero.

In an embodiment of the present invention, the driving mechanism 200 wasdesigned to provide 6.3 kN load (plus 30% margin) to move the magnetarray 114. Furthermore, the driving mechanism 200 controls the phase ofthe movable magnet array with 7.2 kN thrust load capacity. It iscomprised of a 5 mm lead, non-preloaded ball-screw supported by dualpreloaded angular contact bearings. Actuation is achieved with open loopstepper motor positioning through a 7:1 helical gear set. The rodcomponent 202 may be guided by plain bronze linear bearings. It has aspecified repeatability of 25 μm and 250 μm of backlash. Because theloading due to the longitudinal component of the magnetic field isunidirectional, with standard backlash correction routines in the motorcontroller, the backlash may not be problematic.

The present undulator may have a magnetic field similar to conventionalPPM planar undulators, may be approximately 10 times smaller in thetransverse direction and weighs around 80 kg per meter of length. Tocontrol magnetic field strength, the design may use an adjustable phase(AP) scheme.

In an embodiment of the present invention, the basic properties of theundulator 100 are listed below in Table 1.

TABLE 1 Magnetic structure Pure permanent magnet (PPM) Magnetic materialNd—Fe—B, grade 40UH Period 24.4 mm Gap 5 mm - constant vertical gap Peakfield 1.1 Tesla Length 1 m x-ray polarization Linear Transfer dimensionsW × H 148 mm × 156 mm Weight ~62 kg per 1 m length

The outside frame dimensions of the undulator may be 148 mm×156 mm. Theundulator may be 1 meter long, and may have a 5 mm constant gap. Themagnetic field strength may be controlled by an array longitudinalmotion (adjustable phase scheme). The magnetic structure may have a 24.4mm period and maximum magnetic peak field 1.1 Tesla. According to thepresent invention, the undulator 100 can provide similar x-ray beamintensities and variable spectra as conventional undulators. Moreover,the undulator of the present invention is much less expensive thanconventional undulators.

The undulator may be enclosed in a 273 mm (10.75″) diameter cylindricalvacuum vessel while the driving mechanism 200 responsible for moving themagnet array 114 is placed outside the vessel. Following is a discussionof the undulator 100 according to the present invention in terms of itsmechanical, magnetic and vacuum properties, and results of magneticfield measurements as well as properties of the radiated x-ray beam.

Prior to assembly both magnet arrays 114 are individually tuned tominimize optical phase errors and beam trajectory distortion, forexample, tuning may be performed by a small, about 0.1 mm, displacementof individual magnet blocks in a vertical direction.

The quality of the undulator according to the present invention and themagnet operation were confirmed in three experiments discussed below.

In the first experiment, access to the magnetic field region though thevent hole in a side plate was used to measure the field profile in a 33mm span for various phases/positions of the upper array. The array wasmoved by a stepper motor driver. Results are illustrated in FIG. 4 andFIG. 5.

FIG. 4 illustrates a graph of measured field profiles as a function ofthe upper array position. The set of field profiles measured as theupper array was moved by a 1 mm or 14.880 step starting from zero. Thefirst, 00, profile indicated a maximum 1.1 T peak field. The lastprofile taken at 169.70 exhibits a 0.12 T amplitude which is close toexpected 0.099 T. The small difference can be explained by Hall sensormisalignment.

FIG. 5 illustrates a graph of measured K parameters as a function of theupper array position. The measured field profiles were used to calculateundulator K parameter. The profile was approximated by a sine functionwith three free parameters: amplitude B₀, period λ and phase. B₀ and λ pare used to calculate K as:

K=93.4×B ₀ [T]×λ[m]

The solid circles of FIG. 5 depict the K parameter as a function of thearray position. In this experiment, the array was moved by about a 0.5mm/7.44° step. After each step, the field profile was measured and a Kparameter was calculated. The lower plot indicates maximum K value of2.588 at zero phase and close to zero at 180°. Note that the measured Kmaximum is approximately 2% higher than that predicted by the model.There are two possible sources of the discrepancy—the calibration of theHall probe and the difference between the magnetic materialmagnetization used in model (Br=1.26 T) and the real value.

To verify repeatability of the K parameter, the measurements wererepeated a few times. Diamonds on the plot show the normalized Kvariation, dK/K, over four data sets relative to the first one. Steppermotor steps were used as the array position variable. The data indicatethe dK/K repeatability at the level of 5e-4, which is very satisfactoryfor the planned undulator application. The use of a precise encoder inarray position control provides improved repeatability.

In the second experiment, to get full length access to the magneticfield region, one of the side plates was removed and C-clamps wereattached to prevent frame distortion.

In this arrangement, the vertical magnetic field was measured along thebeam axis for various upper array positions as well as the verticalfield variation in the horizontal and vertical directions.

FIG. 6 depicts vertical magnetic field versus position along the magnetarray for 0°, 93.7° and 177.6° phases. In the first case, the averagedpeak field was 1.1177 T, which is in very good agreement with the modelprediction. At 93.7°, the measurement indicated a 0.7603 T averaged peakfield which is also consistent with the model. The RMS optical phaseerrors for both, the 0° and 93.7° fields, were around 3.4°.

To demonstrate that the field quality is adequate for the plannedapplication, the x-ray flux density was calculated as a function ofphoton energy using the Cornell Electron Storage Ring electron beamparameters for the measured and ideal fields and compared. Results areillustrated in FIG. 7 and FIG. 8. The flux generated by G-line wigglerin the present conditions was added to illustrate the anticipated gain.

Small difference between flux densities at 1-st, 3-d and 5-th undulatorharmonics calculated for measured and ideal fields confirms that theundulator field is satisfactory.

The field roll-off in the horizontal direction for all 68 poles wasmeasured and it was found that the variation can be described as

dB _(y) /B _(y)=−(1.98±0.49)×10⁻⁴ δx ²−(3.42±0.63)×10⁻⁶ δx ⁴

where δx is in mm. Mean values of the measured coefficients agree withpredicted values insuring that the averaged dimensions of the permanentmagnet blocks are consistent with the dimensions used in the model andthat the tolerance on the beam orbit stability derived from the modelfield is relevant. The relatively large spread in coefficients is due toa real spread in the magnet blocks.

The vacuum properties of the in-vacuum undulator are critical. Toevaluate vacuum properties of the undulator, both fully assembled magnetarrays were baked in a special constructed vacuum vessel.

To minimize potential damage (demagnetization) of the permanent magnetblocks by elevated temperature, the baking temperature was limited to70° C. The baking time was about 100 hrs. The vacuum pumping during thevacuum tests was provided by a turbo-molecular pump and 75 l/sec ionpump. An ultimate pressure of about 5×10⁻⁹ torr was reached after thebakeout for both magnet arrays. Residual gas analyzer (RGA) data alsoshowed very clean mass spectra, dominated by hydrogen, as illustrated inFIG. 9.

To further evaluate vacuum outgassing of the baked magnet arrays, arate-of-rise measurement was done after the bakeout. With all pumpstuned off, a 2.6 nTorr/sec of the rate of pressure rise is observed.With this measured rate-of-rise and 38.4 liters of vacuum vessel volume,the outgassing rate for one magnet array is estimated to be ˜1.0×10⁻⁷Torr*liter/sec.

In the third experiment undulator was tested with 5 GeV electron beam inCornell Electron Storage Ring. Specifically, two aspects of undulatoroperation were evaluated—undulator radiation properties werecharacterized and undulator interaction with storage ring beams wasevaluated.

For x-ray spectra measurement, an on-axis 0.2×0.2 mm slit 18.3 mdownstream of the undulator and 2 m upstream of the double-bounce Si-111monochromator was defined. The monochromator energy was scanned over arange of 8.6 to 25 keV, measuring the rocking curve of the secondmonochromator crystal at each energy. The x-ray flux was measured usinga nitrogen-filled ion chamber. The measured ion chamber counts werenormalized to the storage ring current. The flux was computed fromtheoretical ion chamber sensitivity based on the photo absorption crosssection for nitrogen and a W-value of 34.6 eV/ion pair. This measuredflux was then finally corrected for sources of attenuation along thebeam axis, including beryllium windows, graphite filter, helium flightpath, and air.

The resulting measured and calculated x-ray spectra are presented inFIG. 10. At the time of measurement the undulator was tuned to 71.350phase (K=2.130) to move third harmonic's energy slightly above 10 keV.An ideal undulator magnetic field was assumed in the calculations. A 1%coupling and beam current was also assumed. As shown in FIG. 10, thegood agreement between measured and predicted undulator spectra up to7-th harmonics indicated satisfactory undulator magnetic field quality.

Undulator K parameter reproducibility is very critical to the operation.It directly depends on accuracy of the mechanical motion. To evaluatethis, the monochromator was set to 30.491 keV photon energy and a numberof undulator scans were made in the range from 121.69 to 123.56 degrees(K parameter was changing from 1.2763 to 1.2388). In this range, the5-th harmonic of undulator radiation is crossing the selected energy andthe dependence of the peak locations of photon counting rate onundulator phase can be used for the reproducibility evaluation. Dataobtained from six scans are illustrated in FIG. 11.

The results reveal 1.4×10⁻⁴ of K variation. Any presence of ˜10 micronsbacklash when the undulator is moving may be avoided if the undulator ismoved through the standard path.

One of the properties of an adjustable phase undulator is theindependence of the beam focusing on K parameter. To check it, theelectron beam tunes as a function of K were measured. The measurementresults, together with vertical tune variation calculated for variablegap undulator, are illustrated in FIG. 12. The data confirms that in anAP structure the K parameter change does not affect storage ring beamfocusing.

Prior to installation into the storage ring, magnetic field integralswere measured that showed the field integrals variation with K at 0.1 Gmlevel or less. The experimental data indicated peak-to-peak ˜5 micronsorbit variation with K change thereby estimating the upper limit onorbit variation as 2 microns and on the first magnetic field integralchange less than 0.1 Gm.

The described embodiments are to be considered in all respects only asillustrative and not restrictive, and the scope of the invention is notlimited to the foregoing description. Those of skill in the art willrecognize changes, substitutions, adaptations and other modificationsthat will nonetheless come within the scope of the invention and rangeof the invention.

1. An undulator system, comprising: a frame comprising a moveablemagnetic array opposing a stationary magnetic array, each magnetic arraycomprising a plurality of holders horizontally arranged with each holdersecuring a magnetized permanent magnet: and a driving mechanismconnected to the moveable magnetic array, the driving mechanismcomprising a rod component moveable within a tube component to move themoveable magnetic array along a horizontal beam axis with respect to thestationary magnetic array.
 2. The undulator system according to claim 1wherein the frame is a box-shape frame.
 3. The undulator systemaccording to claim 1 wherein the magnetized permanent magnet is solderedto each holder.
 4. The undulator system according to claim 1 whereineach magnetic array includes a pair of base plates, the pair of baseplates securing the plurality of holders.
 5. The magnet array of theundulator system according to claim 1 wherein each holder comprises acopper material.
 6. The magnet array of the undulator system accordingto claim 1 wherein the magnetized permanent magnet is a neodymiummagnet.
 7. The undulator system according to claim 1 further comprisinga cooling element attached to the frame for controlling temperature ofthe magnet array.
 8. The undulator system according to claim 7 whereinthe cooling element comprises a coolant of either water or coldnitrogen.
 9. The undulator system according to claim 1 wherein thedriving mechanism moves the moveable magnetic array by a half period(12.2 mm) along a horizontal beam axis with respect to the stationarymagnetic array.
 10. The undulator system according to claim 1 whereineach magnetic array is covered with nickel plated copper foil.
 11. Theundulator system according to claim 1 further comprising a plurality ofminiature linear bearings attached to the moveable magnetic array. 12.An undulator system, comprising: a frame consisting of two arrays, amoveable magnetic array opposing a stationary magnetic array forming agap between the arrays, each magnetic array comprising a plurality ofholders horizontally arranged with a magnetized permanent magnet securedto each holder; a plurality of miniature linear bearings positionedwithin the frame, each miniature linear bearing fastened to the moveablemagnetic array; and a driving mechanism connected to the moveablemagnetic array, the driving mechanism comprising a rod componentmoveable within a tube component activating the plurality of miniaturelinear bearings to move the moveable magnetic array along a horizontalbeam axis with respect to the stationary magnetic array.
 13. Theundulator system according to claim 12 wherein the gap is a constantvertical gap.
 14. The undulator system according to claim 13 wherein theconstant vertical gap is 5 mm.
 15. The undulator system according toclaim 12 wherein the frame is a box-shape frame.
 16. The undulatorsystem according to claim 12 further comprising a cooling elementattached to the frame for controlling temperature of the magnet array.17. The undulator system according to claim 16, the cooling elementcomprising a coolant of either water or cold nitrogen.
 18. The undulatorsystem according to claim 12 wherein each holder comprises a coppermaterial.
 19. The magnet array of the undulator system according toclaim 12 wherein the magnetized permanent magnet is a neodymium magnet.20. The undulator system according to claim 12 wherein each magneticarray is covered with nickel plated copper foil.